Communications in Statistics: Theory and Methods

doi: 10.1080/03610929308831001pmid: N/A

Chakraborti, S.; Gibbons, Jean D.

doi: 10.1080/03610929308831002pmid: N/A

Previously two nonparametric tests were proposed for one-sided comparison of k treatments with a known standard in the one-way layout. The tests are based on (1) the sum, and (2) the minimum, of the k individual one-sided sign test statistics. In this paper we give expressions for the size and power of each test. For specified size and power these formulas are solved simultaneously to determine the minimum sample size and corresponding rejection region for each test. Large sample solutions based on the normal approximation are also given. Specific tables of exact and approximate solutions, are given for k = 2 treatments.

Angus, John E.

doi: 10.1080/03610929308831003pmid: N/A

This paper considers asymptotic analysis of bootstrap distributions for the extremes from an iid sample. In contrast to the case of almost sure convergence to a fixed (normal) distribution in the case of the sample mean (finite variance case), the bootstrap distribution of an extreme tends in distribution to a random probability measure. These results are similar to the result for the bootstrap distribution of the sample mean in the infinite variance case where the underlying random variables are in the domain of attraction of a stable law with index αε(0,2).

Gastaldi, Tommaso; Gastaldi, Tommaso

doi: 10.1080/03610929308831004pmid: N/A

We present a procedure to carry out the Kolmogorov-Smimov (K-S) tests of identity in the case when one possibly censored or truncated sample is involved. The form of censoring we allow is the most general one. Some applications are given.

Whitcomb, Kathleen M.; Lahiff, Maureen

doi: 10.1080/03610929308831005pmid: N/A

Approximate and exact influence functions are investigated for the Shrunken D or DS method of estimating the optimum error rate in a linear discriminant analysis with two populations. Two- and three-dimensional plots of these functions are constructed to illustrate regions where influential observations are most harmful. The extension of these results to higher dimensional cases are discussed. As expected, influence function values reveal that the impact of a perturbing point increases as sample size decreases. Influence function values are more extreme (higher and lower over the range of perturbed observations studied) when the Mahalanobis1 distance between the means are smaller. For sample sizes of 100 or less from each group, the exact expression for the inverted perturbed covariance matrix should be used when constructing the influence function.

Shalaby, O.A.

doi: 10.1080/03610929308831006pmid: N/A

Point and confidence intervals for the scale parameter θ and the reliability function R(to) of the doubly truncated and censored exponential distribution are considered using inverted gamma as a prior distribution for θ. The Bayes risk of Bayesian and non-Bayesian estimators are obtained for comparison. Illustrative examples, using real data are included.

Norris, lll, James L.; Meeter, Duane A.

doi: 10.1080/03610929308831007pmid: N/A

Under both simple random sampling and stratified random sampling from a study region, we develop a Bayesian, asymptotic lower limit for the expected number of the region's classes that are not observed in the sample. In practical applications, the classes might be species in a forest or types of defects in a product line. The aforementioned lower limit is extremely robust to the prior on θ, the total number of classes in the region. We also consider a potential lower limit for θ. Both the lower limit on the expected number of unobserved classes and the lower limit on θ were conservative in our simulations.

Parsian, A.; Sanjari Farsipour, N.; Nematollahi, N.

doi: 10.1080/03610929308831008pmid: N/A

Estimation of location parameter under the asymmetric LINEX loss function is considered with restriction to the principle of invariance. An explicit form of best location-invariant estimator under LINEX loss, which we refer to it as Pitman-type estimator, is obtained and the minimaxity of such estimators is proved.

Henze, Norbert

doi: 10.1080/03610929308831009pmid: N/A

Let X1,…,Xn be independent and identically distributed non-negative random variables, and let Yj = XjXn (j= 1,…,n), where If X1 has the exponential density λexp(−λx),x>0, for some λ>0, the empirical Laplace transform of Y1,…,Yn should be close to (1 + t)−1 which is the Laplace transform of the unit exponential distribution. We study the properties of as a statistic for testing for exponentiality. The limiting null distribution of Tn,a is found, and it is shown that the test rejecting the hypothesis of exponentiality for large values of Tn,a is consistent against each fixed alternative distribution. This new class of tests offers great flexibility in that the parameter a may be chosen so as to yield high power against specific alternatives. It is also possible to let a depend on X1,…, Xn. Power performance of the new tests for finite samples is assessed in a Monte Carlo study.

Rahman, M. S.; Gupta, R. P.

doi: 10.1080/03610929308831010pmid: N/A

A special class of the exponential family of distributions named the family of Transformed Chi-square distributions is defined. Explicit expressions for the minimum variance unbiased estimator with minimum variance of a function of the parameter of this family are given. The critical region and the power function for various tests of hypotheses for the parameter of this family are also obtained.